We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus Tn, n≥2. We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are ±Id and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for T2, P. Iglesias and G. Lachaud for codimension one foliations on Tn, n≥2, and B. Herrera for transcendent foliations. The theoretical setting of the paper is that of J. M. Souriau’s diffeological spaces.